Calculus I
Course Code: MATH 151/153
Course Description :
This course aims to enhance the understanding of concepts and the development of problem-solving skills in the areas of single variable differential calculus and single variable integral calculus. Topics include limits, continuity, differentiation, curve sketching, optimization, and introductory integration. Functions studied range from simple algebraic and radical expressions to more sophisticated rational, logarithms, exponentials, and trigonometric functions.
Duration :
16 Weeks
Mode of Delivery :
Interactive Live Online Sessions
Lectures :
Number of Lectures Per Month : 8 Lectures
Number of Tutorials Per Month : 2 Tutorials (Including Revision Classes for Midterm and Final Exams)
Jai Kumar Verma
Aerospace Engineer
Number of Classes
Lectures
8
Number of Classes
Tutorial
2
Per Month
Total Classes
10
Price Per Month
Group Classes
25
BD
Price Per Month
Private
40
BD
Module Learning Outcomes
By the end of this course, students should be able to
- Understand the meaning of the limit of a function and its importance in calculus.
- Interpret limits graphically and numerically.
- Determine the existence of a limit using various methods.
- Apply the limit laws to compute limits.
- Use the Sandwich Theorem to evaluate limits of functions.
- Understand the concept of one-sided limits and how they differ from two-sided limits.
- Compute one-sided limits and interpret their meaning.
- Apply the concept of one-sided limits to the special case of sin(𝑥)/𝑥 as 𝑥 approaches 0.
- Apply the Intermediate Value Theorem to show the existence of roots in a continuous function.
- Define the continuity of a function and understand its significance in calculus.
- Determine whether a function is continuous at a point or over an interval.
- Extend the concept of continuity to include functions that can be made continuous by redefining values at specific points.
- Explore the continuity of composite functions.
- Understand the concept of finite limits as 𝑥 approaches infinity.
- Determine horizontal asymptotes by finding limits at infinity.
- Identify vertical asymptotes where the function becomes unbounded.
- Understand and compute infinite limits for functions as they approach a point.
- Understand the geometric interpretation of a derivative as a slope of a tangent line.
- Differentiate between secant lines and tangent lines in terms of limits.
- Calculate the derivative of a function using its definition.
- Use different notations for derivatives and understand higher-order derivatives.
- Differentiate trigonometric functions using standard differentiation formulas.
- Apply differentiation rules, including the product, quotient, and chain rule, to various functions.
- Understand the relationship between basic trigonometric functions and their derivatives.
- Understand and apply implicit differentiation to find derivatives of functions defined implicitly.
- Solve problems involving both 𝑥 and 𝑦 that require implicit differentiation.
- Understand the concept of inverse functions and their derivatives.
- Differentiate logarithmic functions using logarithmic differentiation.
- Find derivatives of inverse trigonometric functions and apply them to solve problems.
- Use derivatives to solve problems involving related rates of change.
- Understand and apply the concept of linear approximation to estimate function values.
- Utilize differentials to approximate changes in functions.
- Calculate anti-derivatives of basic functions.
- Solve real-life problems involving anti-derivatives, such as those in physics.
- • Understand the definition of the definite integral and its properties.
- Differentiate between differentiation and integration as inverse processes.
- Apply the Fundamental Theorem of Calculus to evaluate definite integrals.
- Differentiate between definite and indefinite integrals.
- Apply the substitution method to evaluate indefinite integrals.
- Use integration to find the area between curves.
- Determine local and global maximum and minimum values of functions.
- Apply the Extreme Value Theorem in finding extreme values.
- • Understand the concept of monotonic functions and how to test for increasing and decreasing behavior.
- Use the first derivative test to find relative maxima and minima.
- Determine concavity and use it to sketch graphs of functions.
- Apply derivatives to solve optimization problems involving area, perimeter, and other real-world scenarios.
Course Outline
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